Let `f(x) = x^2` and g(x) = 2x + 1 be two real functions. Find : (f + g) (x), (f-g)(x), (fg) (x) and `(f/g)` (x).

Let f(x)= sqrtx and g (x) = x be two functions defined over the set of non-negative real numbers. Find (f+ g) (x), (f-g)(x), (fg) (x) and (f/g) (x).

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If f(x) = x+1 And g (X) = 2x, then f (g(x)) is equal to

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+ (g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be

Let f and g be two functions defined by f(x) = sqrt(x-1) and g(x)= sqrt (4-x^2) . Find : fg .

Let f and g be two functions defined by f(x) = sqrt(x-1) and g(x)= sqrt (4-x^2) . Find : f/g .

If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x) is

Let f and g be two functions defined by f(x) = sqrt(x-1) and g(x)= sqrt (4-x^2) . Find : f - g .